# A Tannakian classification of torsors on the projective line

## TL;DR

This paper provides a Tannakian proof of Grothendieck-Harder’s theorem, classifying torsors under reductive groups on the projective line over a field, offering a new perspective on this classical result.

## Contribution

It introduces a Tannakian approach to prove the classification theorem, offering a novel proof technique compared to traditional methods.

## Key findings

- Tannakian formalism applies to torsor classification.
- Provides a new proof of Grothendieck-Harder theorem.
- Enhances understanding of reductive group torsors.

## Abstract

In this small note we present a Tannakian proof of the theorem of Grothendieck-Harder on the classification of torsors under a reductive group on the projective line over a field.